Defective colorings on complete bipartite and multipartite k-Uniform hypergraphs

Abstract

In this thesis, we modify the definition of a defective coloring and a defective chromatic number on graphs to a defective coloring and a defective chromatic number on hypergraphs. First, we find the defective chromatic number on a complete bipartite k-uniform hypergraph and the defective chromatic number on a complete bipartite k-uniform hypergraph of which each color class is acyclic. Second, we determine the defective chromatic number and the defective chromatic number of which each color class is acyclic on a complete k-partite k-uniform hypergraph whose each edge has k vertices from k different partite sets. Finally, we determine the upper bound of the defective chromatic numbers and determine the defective chromatic number of which each color class is acyclic on a complete tripartite 3-uniform hypergraph whose each edge has three vertices from at least two different partite sets.